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2026
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In this paper, using mappings of the unit ball in \(\mathbb{R}^n\), associated with orthogonal matrices, two types of nonlocal analogues of the polyharmonic operator are introduced. Spectral problems for the Dirichlet problem and Dirichlet-type problems for these operators are studied. The eigenfunctions and eigenvalues of the problems under consideration are found. Theorems on the completeness of systems of eigenfunctions in the space \(L_2\) are proved.